Both of the above plugins (alignment and wrap) allow for aligned paragraphs. However, in one case, the code is not really human-readable -- it's non-intuitive to someone unfamiliar with the plugin. In the second case, the amount of text is quite long for something that I want to be able to use very often.

Did you try the divalign2 plugin? It uses a very simple and mnemonic syntax. As for extending bbcode, since I am maintaining it I plan to enable paragraph alignment with the same tags used in most forums: [left], [center] and [right]. As for how: via using divalign2 when it is available (no sense in reinventing the wheel); as for when: when I have the time.